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cemmap Working Papers
October 2012 CWP31/12
Article
Asymptotic efficiency of semiparametric two-step GMM
Type: cemmap Working Papers
Authors: Xiaohong Chen, Jinyong Hahn and Zhipeng Liao
JEL classification: C14, C31, C32
Keywords: Overlapping information sets, semiparametric efficiency, two-step GMM

In this note, we characterise the semiparametric efficiency bound for a class of semiparametric models in which the unknown nuisance functions are identified via nonparametric conditional moment restrictions with possibly non-nested or over-lapping conditioning sets, and the finite dimensional parameters are potentially over-identified via unconditional moment restrictions involving the nuisance functions. We discover a surprising result that semiparametric two-step optimally weighted GMM estimators achieve the efficiency bound, where the nuisance functions could be estimated via any consistent non-parametric procedures in the first step. Regardless of whether the efficiency bound has a closed form expression or not, we provide easy-to-compute sieve based optimal weight matrices that lead to asymptotically efficient two-step GMM estimators.

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